Abstract

Holographic imaging has proved to be useful for spherical particle characterization, including the retrieval of particle size, refractive index, and 3D location. In this method, the interference pattern of the incident and scattered light fields is recorded by a camera and compared with the relevant Lorenz–Mie solutions. However, the method is limited to spherical particles, and the complete polarized scattering components have not been studied. This work extends the Mueller matrix formalism for the scattered light to describe the interference light field, and proposes a Mueller matrix holography method, through which complete polarization information can be obtained. The mathematical formalism of the holographic Mueller matrix is derived, and numerical examples of birefringent spheres are provided. The Mueller matrix holography method may provide a better opportunity than conventional methods to study anisotropic particles.

© 2013 Optical Society of America

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2012 (2)

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

M. Gao, Y. You, P. Yang, and G. W. Kattawar, “Backscattering properties of small layered plates: a model for iridosomes,” Opt. Express 20, 25111–25120 (2012).
[CrossRef]

2011 (5)

M. J. Berg and G. Videen, “Digital holographic imaging of aerosol particles in flight,” J. Quant. Spectrosc. Radiat. Transfer 112, 1776–1783 (2011).
[CrossRef]

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matt. 7, 6816–6819 (2011).
[CrossRef]

K. Kuroda, Y. Matsuhashi, R. Fujimura, and T. Shimura, “Theory of polarization holography,” Opt. Rev. 18, 374–382 (2011).
[CrossRef]

H.-Z. Liu, J. L.-W. Li, M. S. Leong, and S. Zouhdi, “Transparent uniaxial anisotropic spherical particles designed using radial anisotropy,” Phys. Rev. E 84, 016605 (2011).
[CrossRef]

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transfer 112, 2234–2247 (2011).
[CrossRef]

2010 (2)

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[CrossRef]

G. W. Graham and W. A. M. N. Smith, “The application of holography to the analysis of size and settling velocity of suspended cohesive sediments,” Limnol. Oceanogr. 8, 1–15 (2010).

2009 (2)

L. M. Mäthger, E. J. Denton, N. J. Marshall, and R. T. Hanlon, “Mechanisms and behavioural functions of structural coloration in cephalopods,” J. R. Soc. Interface 6, S149–S163 (2009).
[CrossRef]

X. Wu, G. GrÈhan, S. Meunier-Guttin-Cluzel, L. Chen, and K. Cen, “Sizing of particles smaller than 5 μm in digital holographic microscopy,” Opt. Lett. 34, 857–859 (2009).
[CrossRef]

2007 (1)

2006 (2)

2005 (1)

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

2004 (1)

2003 (1)

2000 (1)

1998 (1)

E. S. Thiele and R. H. French, “Computation of light scattering by anisotropic spheres of rutile titania,” Adv. Mater. 10, 1271–1276 (1998).
[CrossRef]

1997 (1)

1996 (1)

1992 (1)

K. L. Wong and H. T. Chen, “Electromagnetic scattering by a uniaxially anisotropic sphere,” IEE Proc. Microw. Anten. Propag. 139, 314–318 (1992).
[CrossRef]

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

1985 (1)

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

1984 (1)

1980 (1)

1978 (1)

1974 (1)

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E 7, 781–788 (1974).
[CrossRef]

1973 (2)

A. J. Hunt and D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[CrossRef]

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

1951 (1)

Allano, D.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz–Mie theory and its application to microholography,” Appl. Opt. 23, 4140–4148 (1984).
[CrossRef]

Asundi, A. K.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[CrossRef]

Bailey, W. M.

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Bass, M.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed., Vol. IV of Optical properties of materials, nonlinear optics, quantum optics (McGraw-Hill, 2010).

Bell, G. R. R.

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

Berg, M. J.

M. J. Berg and G. Videen, “Digital holographic imaging of aerosol particles in flight,” J. Quant. Spectrosc. Radiat. Transfer 112, 1776–1783 (2011).
[CrossRef]

Bickel, W. S.

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2004).

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Bottiger, J. R.

Brunel, M.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

Cen, K.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

X. Wu, G. GrÈhan, S. Meunier-Guttin-Cluzel, L. Chen, and K. Cen, “Sizing of particles smaller than 5 μm in digital holographic microscopy,” Opt. Lett. 34, 857–859 (2009).
[CrossRef]

Cen, K. F.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Chen, H. T.

K. L. Wong and H. T. Chen, “Electromagnetic scattering by a uniaxially anisotropic sphere,” IEE Proc. Microw. Anten. Propag. 139, 314–318 (1992).
[CrossRef]

Chen, L.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

X. Wu, G. GrÈhan, S. Meunier-Guttin-Cluzel, L. Chen, and K. Cen, “Sizing of particles smaller than 5 μm in digital holographic microscopy,” Opt. Lett. 34, 857–859 (2009).
[CrossRef]

Cheong, F. C.

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matt. 7, 6816–6819 (2011).
[CrossRef]

Coetmellec, S.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

Crookes-Goodson, W. J.

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

Darakis, E.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[CrossRef]

DeCusatis, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed., Vol. IV of Optical properties of materials, nonlinear optics, quantum optics (McGraw-Hill, 2010).

Dennis, P. B.

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

Denton, E. J.

L. M. Mäthger, E. J. Denton, N. J. Marshall, and R. T. Hanlon, “Mechanisms and behavioural functions of structural coloration in cephalopods,” J. R. Soc. Interface 6, S149–S163 (2009).
[CrossRef]

Devore, J. R.

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Enoch, J.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed., Vol. IV of Optical properties of materials, nonlinear optics, quantum optics (McGraw-Hill, 2010).

French, R. H.

E. S. Thiele and R. H. French, “Computation of light scattering by anisotropic spheres of rutile titania,” Adv. Mater. 10, 1271–1276 (1998).
[CrossRef]

Fry, E. S.

Fugal, J. P.

Fujimura, R.

K. Kuroda, Y. Matsuhashi, R. Fujimura, and T. Shimura, “Theory of polarization holography,” Opt. Rev. 18, 374–382 (2011).
[CrossRef]

Gao, M.

M. Gao, Y. You, P. Yang, and G. W. Kattawar, “Backscattering properties of small layered plates: a model for iridosomes,” Opt. Express 20, 25111–25120 (2012).
[CrossRef]

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

M. Gao, P. Yang, and G. W. Kattawar, “Polarized extinction properties of plates with large aspect ratios “ J. Quant. Spectrosc. Radiat. Transfer (2013, to be published).

Gouesbet, G.

Graham, G. W.

G. W. Graham and W. A. M. N. Smith, “The application of holography to the analysis of size and settling velocity of suspended cohesive sediments,” Limnol. Oceanogr. 8, 1–15 (2010).

Grehan, G.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz–Mie theory and its application to microholography,” Appl. Opt. 23, 4140–4148 (1984).
[CrossRef]

GrÈhan, G.

Grier, D. G.

Hanlon, R. T.

L. M. Mäthger, E. J. Denton, N. J. Marshall, and R. T. Hanlon, “Mechanisms and behavioural functions of structural coloration in cephalopods,” J. R. Soc. Interface 6, S149–S163 (2009).
[CrossRef]

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transfer 112, 2234–2247 (2011).
[CrossRef]

Huffman, D. R.

R. J. Perry, A. J. Hunt, and D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978).
[CrossRef]

A. J. Hunt and D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[CrossRef]

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2004).

Hunt, A. J.

R. J. Perry, A. J. Hunt, and D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978).
[CrossRef]

A. J. Hunt and D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[CrossRef]

Jiao, S.

Karaveli, S.

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

Kariwala, V.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[CrossRef]

Kattawar, G. W.

M. Gao, Y. You, P. Yang, and G. W. Kattawar, “Backscattering properties of small layered plates: a model for iridosomes,” Opt. Express 20, 25111–25120 (2012).
[CrossRef]

C. Li, G. W. Kattawar, and P. Yang, “Identification of aerosols by their backscattered Mueller images,” Opt. Express 14, 3616–3621 (2006).
[CrossRef]

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

M. Gao, P. Yang, and G. W. Kattawar, “Polarized extinction properties of plates with large aspect ratios “ J. Quant. Spectrosc. Radiat. Transfer (2013, to be published).

Katz, J.

Khanam, T.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[CrossRef]

Kim, S.-H.

Kuroda, K.

K. Kuroda, Y. Matsuhashi, R. Fujimura, and T. Shimura, “Theory of polarization holography,” Opt. Rev. 18, 374–382 (2011).
[CrossRef]

Kuzirian, A. M.

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

Lakshminarayanan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed., Vol. IV of Optical properties of materials, nonlinear optics, quantum optics (McGraw-Hill, 2010).

Lebrun, D.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Lee, S.-H.

Leong, M. S.

H.-Z. Liu, J. L.-W. Li, M. S. Leong, and S. Zouhdi, “Transparent uniaxial anisotropic spherical particles designed using radial anisotropy,” Phys. Rev. E 84, 016605 (2011).
[CrossRef]

Li, C.

Li, G.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed., Vol. IV of Optical properties of materials, nonlinear optics, quantum optics (McGraw-Hill, 2010).

Li, J. L.-W.

H.-Z. Liu, J. L.-W. Li, M. S. Leong, and S. Zouhdi, “Transparent uniaxial anisotropic spherical particles designed using radial anisotropy,” Phys. Rev. E 84, 016605 (2011).
[CrossRef]

Liou, K. N.

P. Yang and K. N. Liou, “Light scattering by hexagonal ice crystals: solutions by a ray-by-ray integration algorithm,” J. Opt. Soc. Am. A 14, 2278–2289 (1997).
[CrossRef]

P. Yang and K. N. Liou, “Geometric-optics integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef]

P. Yang and K. N. Liou, “Finite difference time domain method for light scattering by nonspherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).

Liu, H.-Z.

H.-Z. Liu, J. L.-W. Li, M. S. Leong, and S. Zouhdi, “Transparent uniaxial anisotropic spherical particles designed using radial anisotropy,” Phys. Rev. E 84, 016605 (2011).
[CrossRef]

MacDonald, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed., Vol. IV of Optical properties of materials, nonlinear optics, quantum optics (McGraw-Hill, 2010).

Mahajan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed., Vol. IV of Optical properties of materials, nonlinear optics, quantum optics (McGraw-Hill, 2010).

Malek, M.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Malkiel, E.

Marshall, N. J.

L. M. Mäthger, E. J. Denton, N. J. Marshall, and R. T. Hanlon, “Mechanisms and behavioural functions of structural coloration in cephalopods,” J. R. Soc. Interface 6, S149–S163 (2009).
[CrossRef]

Mäthger, L. M.

L. M. Mäthger, E. J. Denton, N. J. Marshall, and R. T. Hanlon, “Mechanisms and behavioural functions of structural coloration in cephalopods,” J. R. Soc. Interface 6, S149–S163 (2009).
[CrossRef]

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

Matsuhashi, Y.

K. Kuroda, Y. Matsuhashi, R. Fujimura, and T. Shimura, “Theory of polarization holography,” Opt. Rev. 18, 374–382 (2011).
[CrossRef]

Meng, H.

Meunier-Guttin-Cluzel, S.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

X. Wu, G. GrÈhan, S. Meunier-Guttin-Cluzel, L. Chen, and K. Cen, “Sizing of particles smaller than 5 μm in digital holographic microscopy,” Opt. Lett. 34, 857–859 (2009).
[CrossRef]

Naik, R. R.

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

Naughton, T. J.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[CrossRef]

Pan, G.

Patte-Rouland, B.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Perry, R. J.

Pine, D. J.

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matt. 7, 6816–6819 (2011).
[CrossRef]

Pu, S. L.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Rajendran, A.

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[CrossRef]

Roichman, Y.

Saengkaew, S.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

Saw, E. W.

Senft, S. L.

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

Sergeyev, A. V.

Shaw, R. A.

Sheng, J.

Shimura, T.

K. Kuroda, Y. Matsuhashi, R. Fujimura, and T. Shimura, “Theory of polarization holography,” Opt. Rev. 18, 374–382 (2011).
[CrossRef]

Slimani, F.

Smith, W. A. M. N.

G. W. Graham and W. A. M. N. Smith, “The application of holography to the analysis of size and settling velocity of suspended cohesive sediments,” Limnol. Oceanogr. 8, 1–15 (2010).

Thiele, E. S.

E. S. Thiele and R. H. French, “Computation of light scattering by anisotropic spheres of rutile titania,” Adv. Mater. 10, 1271–1276 (1998).
[CrossRef]

Thompson, B. J.

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E 7, 781–788 (1974).
[CrossRef]

Thompson, R. C.

van Blaaderen, A.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, 1981).

van Oostrum, P.

Van Stryland, E.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed., Vol. IV of Optical properties of materials, nonlinear optics, quantum optics (McGraw-Hill, 2010).

Videen, G.

M. J. Berg and G. Videen, “Digital holographic imaging of aerosol particles in flight,” J. Quant. Spectrosc. Radiat. Transfer 112, 1776–1783 (2011).
[CrossRef]

Wang, L. V.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Wong, K. L.

K. L. Wong and H. T. Chen, “Electromagnetic scattering by a uniaxially anisotropic sphere,” IEE Proc. Microw. Anten. Propag. 139, 314–318 (1992).
[CrossRef]

Wu, X.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

X. Wu, G. GrÈhan, S. Meunier-Guttin-Cluzel, L. Chen, and K. Cen, “Sizing of particles smaller than 5 μm in digital holographic microscopy,” Opt. Lett. 34, 857–859 (2009).
[CrossRef]

Wu, Y.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

Xiao, K.

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matt. 7, 6816–6819 (2011).
[CrossRef]

Yang, P.

Yang, S.-M.

Yao, G.

Yi, G.-R.

You, Y.

Yurkin, M. A.

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transfer 112, 2234–2247 (2011).
[CrossRef]

Zia, R.

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

Zouhdi, S.

H.-Z. Liu, J. L.-W. Li, M. S. Leong, and S. Zouhdi, “Transparent uniaxial anisotropic spherical particles designed using radial anisotropy,” Phys. Rev. E 84, 016605 (2011).
[CrossRef]

Adv. Mater. (1)

E. S. Thiele and R. H. French, “Computation of light scattering by anisotropic spheres of rutile titania,” Adv. Mater. 10, 1271–1276 (1998).
[CrossRef]

Am. J. Phys. (1)

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Appl. Opt. (8)

Astrophys. J. (2)

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Chem. Eng. Sci. (1)

E. Darakis, T. Khanam, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044 (2010).
[CrossRef]

Exp. Fluids (1)

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

IEE Proc. Microw. Anten. Propag. (1)

K. L. Wong and H. T. Chen, “Electromagnetic scattering by a uniaxially anisotropic sphere,” IEE Proc. Microw. Anten. Propag. 139, 314–318 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. E (1)

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E 7, 781–788 (1974).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

M. J. Berg and G. Videen, “Digital holographic imaging of aerosol particles in flight,” J. Quant. Spectrosc. Radiat. Transfer 112, 1776–1783 (2011).
[CrossRef]

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transfer 112, 2234–2247 (2011).
[CrossRef]

J. R. Soc. Interface (1)

L. M. Mäthger, E. J. Denton, N. J. Marshall, and R. T. Hanlon, “Mechanisms and behavioural functions of structural coloration in cephalopods,” J. R. Soc. Interface 6, S149–S163 (2009).
[CrossRef]

Limnol. Oceanogr. (1)

G. W. Graham and W. A. M. N. Smith, “The application of holography to the analysis of size and settling velocity of suspended cohesive sediments,” Limnol. Oceanogr. 8, 1–15 (2010).

Opt. Commun. (1)

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coetmellec, K. Cen, and G. Grehan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020 (2012).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Opt. Rev. (1)

K. Kuroda, Y. Matsuhashi, R. Fujimura, and T. Shimura, “Theory of polarization holography,” Opt. Rev. 18, 374–382 (2011).
[CrossRef]

Phys. Rev. E (1)

H.-Z. Liu, J. L.-W. Li, M. S. Leong, and S. Zouhdi, “Transparent uniaxial anisotropic spherical particles designed using radial anisotropy,” Phys. Rev. E 84, 016605 (2011).
[CrossRef]

Rev. Sci. Instrum. (1)

A. J. Hunt and D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[CrossRef]

Soft Matt. (1)

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matt. 7, 6816–6819 (2011).
[CrossRef]

Other (7)

L. M. Mäthger, S. L. Senft, M. Gao, S. Karaveli, G. R. R. Bell, R. Zia, A. M. Kuzirian, P. B. Dennis, W. J. Crookes-Goodson, R. R. Naik, G. W. Kattawar, and R. T. Hanlon, “Bright white scattering from protein spheres in color changing, flexible cuttlefish skin,” Adv. Funct. Mater. (to be published).

M. Gao, P. Yang, and G. W. Kattawar, “Polarized extinction properties of plates with large aspect ratios “ J. Quant. Spectrosc. Radiat. Transfer (2013, to be published).

P. Yang and K. N. Liou, “Finite difference time domain method for light scattering by nonspherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed., Vol. IV of Optical properties of materials, nonlinear optics, quantum optics (McGraw-Hill, 2010).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2004).

H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, 1981).

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Figures (9)

Fig. 1.
Fig. 1.

Particle is located in plane 1 with a beam of light incident on the particle. Interference pattern is recorded in plane 2. Scattering angle at point P is denoted by (θ,ϕ).

Fig. 2.
Fig. 2.

(a) Birefringent sphere with a radius a and an optical axis along the y direction. The refractive indices along the x, y, and z axes are nx, ny, and nz, where nx=nzny. The incident direction of the light is along +z. (b) Sphere is rotated around the x axis with an orientation angle β, and the optical axis is along the y′ direction. (c) Angular distribution diagram for the holographic Mueller matrix. Zenith angles (θ) from 0° to 40° and azimuthal angles (ϕ) from 0° to 360° are shown.

Fig. 3.
Fig. 3.

Angular distribution [according to Fig. 2(c)] of Mijh for TiO2 with size parameter ka=5.

Fig. 4.
Fig. 4.

Same as Fig. 3 but for an isotropic sphere with nx=ny=nz=1.7.

Fig. 5.
Fig. 5.

Angular distribution of M11h and M12h for a TiO2 sphere with size parameter ka=5 and orientation β=0°, 30°, and 90°. Angular distribution for each element is shown according to Fig. 2(c).

Fig. 6.
Fig. 6.

Same as the M11h and M12h results in Fig. 5, but only for ϕ=0° (solid lines) and ϕ=90° (dashed lines).

Fig. 7.
Fig. 7.

Relative differences of M11h and M12h between ϕ=0° and ϕ=90° for TiO2 spheres at β=0° with size parameters from 1 to 10.

Fig. 8.
Fig. 8.

Mijh for a CaCO3 sphere with ka=5 and β=0°. Angular distribution for each element is shown according to Fig. 2(c).

Fig. 9.
Fig. 9.

Same as Fig. 7 but for CaCO3 spheres.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

I=ElEl*+ErEr*,
Q=ElEl*ErEr*,
U=ElEr*+ErEl*,
V=i(ElEr*ErEl*),
Es(r)=eik(rz)ikrSE0(z),
Is=1k2r2MsI0,
S=eik(rz)ikrS+1,
M=1+1k2r2Ms+1krQ,
Mh=M1=1krQ.
Q=(Q11Q12Q13Q14Q12Q11Q23Q24Q13Q23Q11Q34Q14Q24Q34Q11).
Q11=cosαIm[S11+S22]sinαRe[S11+S22],
Q12=cosαIm[S11S22]sinαRe[S11S22],
Q34=cosαRe[S11S22]sinαIm[S11S22],
Q13=cosαIm[S12+S21]sinαRe[S12+S21],
Q14=cosαRe[S12S21]+sinαIm[S12S21],
Q23=cosαIm[S12S21]sinαRe[S12S21],
Q24=cosαRe[S12+S21]+sinαIm[S12+S21],
(DxDyDz)=(εxx000εyy000εzz)(ExEyEz),
ΔMijh=0θmdθsinθ|Mijh(ϕ=0°,θ)Mijh(ϕ=90°,θ)|0θmdθsinθ|M11h(ϕ=0°,θ)+M11h(ϕ=90°,θ)|,

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